THEMATIC PROGRAMS

Organizing Committee:

Thomas Richardson, University of Warwick
Peter Spirtes, Carnegie Mellon University

Overview:

In many practical applications, a description of the conditional independence
structure does not directly address the substantive questions raised
by researchers. For example, a researcher may be concerned with trying
to discover whether one variable (e.g. cellular phone usage) has a causal
influence on another (e.g. risk of cancer), particularly in contexts
where it is not possible to carry out randomized controlled experiments.

Such an analysis faces considerable problems: first, there may be many different
causal models that are compatible with a given conditional independence structure
'correlation is not causation'; second, in most situations there may be many
causally relevant quantities that have not been measured (often called 'confounding
variables'). The first problem poses difficulties for any approach which begins
by considering a particular causal model: compatibility of the hypothesized
model with data in no way precludes the existence of causally different, but
statistically equivalent models, from which one might draw radically different
causal conclusions. The second problem presents difficulties for traditional
methods, such as regression, which typically assume that there are no unmeasured
confounding variables.

Directed graphs are a natural language for exploring such questions since
directed graphs can be used to represent a causal structure (X -> Y iff
'X is a cause of Y') and conditional independence structure, as a graphical
Markov model.

The purpose of this seminar is to investigate different assumptions relating
causal relations and conditional independence relations and further, to examine
the way in which, given these assumptions, causal structure is underdetermined
by conditional independence structure.